Finite Group Databasebeta

← C29×#29070 #20323970

Subgroups — C29×#29070 #20323970

Order 7424.

716 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2497C211yesmaximal, characteristic
2C29×#2429C211yesmaximal, characteristic
3C29×#2100C211yesmaximal, characteristic, complemented
4C29×#2043C211yesmaximal, characteristic, complemented
5C29×#2035C211yesmaximal, characteristic
6C29×#2035C211yesmaximal, characteristic
7C29×#1956C211yesmaximal, characteristic, complemented
8C29×#1941C211yesmaximal, characteristic, complemented
9C29×#1935C211yesmaximal, characteristic, complemented
10C29×#1927C211yesmaximal, characteristic, complemented
11C29×#1894C211yesmaximal, characteristic
12C29×#1894C211yesmaximal, characteristic
13C29×#1865C211yesmaximal, characteristic, complemented
14C29×#1763C211yesmaximal, characteristic, complemented
15C29×#1753C211yesmaximal, characteristic
16C22×M16×C29C2211yescharacteristic
17C2×C29×C4⋊Q8C2211yescharacteristic
18C2×C29×C22⋊Q8C2211yescharacteristic
19C2×C29×C22⋊Q8C2211yescharacteristic
20C2×C4×Q8×C29C2211yescharacteristic
21C2×C29×#106C2211yescharacteristic
22C2×C29×#106C2211yescharacteristic
23C2×C29×#103C2211yescharacteristic
24C2×C29×#103C2211yescharacteristic
25C2×C29×#103C2211yescharacteristic
26C2×C29×#103C2211yescharacteristic
27C2×C29×#103C2211yescharacteristic
28C2×C29×#103C2211yescharacteristic
29C2×C29×#103C2211yescharacteristic
30C2×C29×#103C2211yescharacteristic
31C2×C29×C22⋊C8C2211yescharacteristic
32C2×C29×#97C2211yescharacteristic
33C2×C4×C8×C29C2211yescharacteristic
34C29×#400—21no—
35C29×#398—21no—
36C29×#396—21no—
37C29×#396—21no—
38C29×#391C2211yescharacteristic
39C29×#389—21no—
40C29×#389C2211yescharacteristic
41C29×#389C2211yescharacteristic
42C29×#389C2211yescharacteristic
43C29×#388—21no—
44C29×#388—21no—
45C29×#387—21no—
46C29×#384C2211yescharacteristic
47C29×#380C2211yescharacteristic
48C29×#380C2211yescharacteristic
49C4×C4⋊C4×C29C2211yescharacteristic
50C4×C22⋊C4×C29C2211yescharacteristic
51C29×#340C2211yescharacteristic
52C29×#340C2211yescharacteristic
53C29×#340C2211yescharacteristic
54C29×#340C2211yescharacteristic
55C29×#340C2211yescharacteristic
56C29×#340C2211yescharacteristic
57C29×#336C2211yescharacteristic
58C29×#336C2211yescharacteristic
59C22×Q8×C29C2311yescharacteristic
60C22×Q8×C29C2311yescharacteristic
61C23×C4×C29C2311yescharacteristic
62C2×M16×C29—22no—
63C2×M16×C29—41no—
64C2×M16×C29—41no—
65C22×C8×C29C2311yescharacteristic
66C22×C8×C29C2311yescharacteristic
67C22×C8×C29C2311yescharacteristic
68C22×C8×C29C2311yescharacteristic
69C29×C4⋊Q8—22no—
70C29×C4⋊Q8—41no—
71C29×C22⋊Q8—22no—
72C29×C22⋊Q8—22no—
73C29×C22⋊Q8—41no—
74C29×C22⋊Q8—41no—
75C4×Q8×C29—22no—
76C4×Q8×C29—41no—
77C2×C4⋊C4×C29—21no—
78C2×C4⋊C4×C29—21no—
79C2×C4⋊C4×C29—21no—
80C2×C4⋊C4×C29—21no—
81C2×C4⋊C4×C29—21no—
82C2×C4⋊C4×C29—21no—
83C2×C4⋊C4×C29—21no—
84C2×C4⋊C4×C29—21no—
85C2×C4⋊C4×C29—21no—
86C2×C4⋊C4×C29—21no—
87C2×C4⋊C4×C29C2311yescharacteristic
88C2×C4⋊C4×C29C2311yescharacteristic
89C2×C4⋊C4×C29C2311yescharacteristic
90C2×C4⋊C4×C29C2311yescharacteristic
91C2×C4⋊C4×C29C2311yescharacteristic
92C2×C4⋊C4×C29C2311yescharacteristic
93C2×C22⋊C4×C29—21no—
94C2×C22⋊C4×C29—21no—
95C2×C22⋊C4×C29—21no—
96C2×C22⋊C4×C29—21no—
97C2×C22⋊C4×C29D411yescharacteristic
98C2×C22⋊C4×C29D411yescharacteristic
99C2×C42×C29—21no—
100C2×C42×C29—21no—
101C2×C42×C29C2311yescharacteristic
102C2×C42×C29C2311yescharacteristic
103C29×#106—22no—
104C29×#106—41no—
105C29×#103—22no—
106C29×#103—22no—
107C29×#103—22no—
108C29×#103—22no—
109C29×#103—22no—
110C29×#103—41no—
111C29×#103—41no—
112C29×#103—41no—
113C29×C22⋊C8—22no—
114C29×#97—41no—
115C4×C8×C29—41no—
116C29×#95—21no—
117C29×#95—21no—
118C29×#95—21no—
119C29×#95—21no—
120C29×#95—21no—
121C29×#95—21no—
122C29×#95—21no—
123C29×#95—21no—
124C29×#95D411yescharacteristic
125C29×#95D411yescharacteristic
126C24×C29C2×D411yescharacteristic
127C2×Q8×C29—21no—
128C2×Q8×C29—21no—
129C2×Q8×C29—21no—
130C2×Q8×C29—21no—
131C2×Q8×C29—21no—
132C2×Q8×C29—21no—
133C2×Q8×C29—21no—
134C2×Q8×C29—21no—
135C2×Q8×C29—21no—
136C2×Q8×C29—21no—
137C2×Q8×C29—21no—
138C2×Q8×C29#4112yes—
139C22×C4×C29—21no—
140C22×C4×C29—21no—
141C22×C4×C29—21no—
142C22×C4×C29—21no—
143C22×C4×C29—21no—
144C22×C4×C29—21no—
145C22×C4×C29—21no—
146C22×C4×C29—21no—
147C22×C4×C29—21no—
148C22×C4×C29—21no—
149C22×C4×C29—21no—
150C22×C4×C29—21no—
151C22×C4×C29—21no—
152C22×C4×C29—21no—
153C22×C4×C29C2×D411yescharacteristic
154C22×C4×C29C2×D411yescharacteristic
155C22×C4×C29C2×D411yescharacteristic
156C22×C4×C29C2×D411yescharacteristic
157C22×C4×C29C2×D411yescharacteristic
158C22×C4×C29C2411yescharacteristic
159M16×C29—44no—
160C2×C8×C29—21no—
161C2×C8×C29—21no—
162C2×C8×C29—21no—
163C2×C8×C29—21no—
164C2×C8×C29—21no—
165C2×C8×C29—21no—
166C2×C8×C29—21no—
167C2×C8×C29—21no—
168C2×C8×C29—21no—
169C2×C8×C29—21no—
170C2×C8×C29#4112yes—
171C2×C8×C29#4112yes—
172C4⋊C4×C29—21no—
173C4⋊C4×C29—21no—
174C4⋊C4×C29—21no—
175C4⋊C4×C29—21no—
176C4⋊C4×C29—21no—
177C4⋊C4×C29—21no—
178C4⋊C4×C29—21no—
179C4⋊C4×C29—21no—
180C4⋊C4×C29—21no—
181C4⋊C4×C29—21no—
182C4⋊C4×C29—21no—
183C4⋊C4×C29—42no—
184C4⋊C4×C29—42no—
185C4⋊C4×C29—42no—
186C4⋊C4×C29—42no—
187C4⋊C4×C29—42no—
188C4⋊C4×C29—42no—
189C4⋊C4×C29—42no—
190C4⋊C4×C29—81no—
191C4⋊C4×C29—81no—
192C4⋊C4×C29—81no—
193C4⋊C4×C29#4112yes—
194C22⋊C4×C29—22no—
195C22⋊C4×C29—22no—
196C22⋊C4×C29—42no—
197C22⋊C4×C29—42no—
198C22⋊C4×C29—81no—
199C22⋊C4×C29—81no—
200C42×C29—21no—
201C42×C29—21no—
202C42×C29—21no—
203C42×C29—21no—
204C42×C29—42no—
205C42×C29—81no—
206#29070C2911yesmaximal, characteristic, direct product factor, Sylow
207C23×C29—21no—
208C23×C29—21no—
209C23×C29—21no—
210C23×C29—21no—
211C23×C29—21no—
212C23×C29—21no—
213C23×C29—21no—
214C23×C29C22×D411yescharacteristic
215Q8×C29—22no—
216Q8×C29—22no—
217Q8×C29—41no—
218Q8×C29—41no—
219Q8×C29—41no—
220Q8×C29—41no—
221Q8×C29—41no—
222Q8×C29—41no—
223C2×C4×C29—21no—
224C2×C4×C29—21no—
225C2×C4×C29—21no—
226C2×C4×C29—21no—
227C2×C4×C29—21no—
228C2×C4×C29—21no—
229C2×C4×C29—21no—
230C2×C4×C29—22no—
231C2×C4×C29—22no—
232C2×C4×C29—21no—
233C2×C4×C29—21no—
234C2×C4×C29—21no—
235C2×C4×C29—21no—
236C2×C4×C29—21no—
237C2×C4×C29—21no—
238C2×C4×C29—41no—
239C2×C4×C29—41no—
240C2×C4×C29—41no—
241C2×C4×C29—41no—
242C2×C4×C29—41no—
243C2×C4×C29—41no—
244C2×C4×C29—41no—
245C2×C4×C29—41no—
246C2×C4×C29—41no—
247C2×C4×C29—41no—
248C2×C4×C29—41no—
249C2×C4×C29—41no—
250C2×C4×C29—41no—
251C2×C4×C29—41no—
252C2×C4×C29—41no—
253C2×C4×C29—41no—
254C2×C4×C29—41no—
255C2×C4×C29—41no—
256C2×C4×C29—41no—
257C2×C4×C29—41no—
258C2×C4×C29—41no—
259C2×C4×C29—41no—
260C2×C4×C29—41no—
261C2×C4×C29—41no—
262C2×C4×C29—41no—
263C2×C4×C29—41no—
264C2×C4×C29#13712yes—
265C2×C4×C29#13712yes—
266C2×C4×C29C2×#4111yescharacteristic
267C2×C4×C29C2×#4111yescharacteristic
268C2×C4×C29C2×#4111yescharacteristic
269C2×C4×C29C2×#4111yescharacteristic
270C2×C4×C29H(5,𝔽2)11yescharacteristic
271C2×C4×C29H(5,𝔽2)11yescharacteristic
272C8×C29—22no—
273C8×C29—22no—
274C8×C29—41no—
275C8×C29—41no—
276#2497C2×C2911yescharacteristic
277#2429C2×C2911yescharacteristic
278#2100C2×C2911yescharacteristic, complemented
279#2043C2×C2911yescharacteristic, complemented
280#2035C2×C2911yescharacteristic
281#2035C2×C2911yescharacteristic
282#1956C2×C2911yescharacteristic, complemented
283#1941C2×C2911yescharacteristic, complemented
284#1935C2×C2911yescharacteristic, complemented
285#1927C2×C2911yescharacteristic, complemented
286#1894C2×C2911yescharacteristic
287#1894C2×C2911yescharacteristic
288#1865C2×C2911yescharacteristic, complemented
289#1763C2×C2911yescharacteristic, complemented
290#1753C2×C2911yescharacteristic
291C22×C29—41no—
292C22×C29—41no—
293C22×C29—41no—
294C22×C29—41no—
295C22×C29—41no—
296C22×C29—41no—
297C22×C29—41no—
298C22×C29#53211yescharacteristic
299C22×C29#54611yescharacteristic
300C22×C29#54611yescharacteristic
301C22×C29C2×#13711yescharacteristic
302C22×C29C2×#13711yescharacteristic
303C22×C29#57711yescharacteristic
304C22×C29#57711yescharacteristic
305C4×C29—22no—
306C4×C29—22no—
307C4×C29—41no—
308C4×C29—41no—
309C4×C29—42no—
310C4×C29—41no—
311C4×C29—42no—
312C4×C29—81no—
313C4×C29—81no—
314C4×C29—81no—
315C4×C29—81no—
316C4×C29—81no—
317C4×C29—81no—
318C4×C29#52911yescharacteristic
319C4×C29#53811yescharacteristic
320C4×C29#55311yescharacteristic
321C4×C29#55311yescharacteristic
322C22×M16C22×C2911yescharacteristic
323C2×C4⋊Q8C22×C2911yescharacteristic
324C2×C22⋊Q8C22×C2911yescharacteristic
325C2×C22⋊Q8C22×C2911yescharacteristic
326C2×C4×Q8C22×C2911yescharacteristic
327C2×#106C22×C2911yescharacteristic
328C2×#106C22×C2911yescharacteristic
329C2×#103C22×C2911yescharacteristic
330C2×#103C22×C2911yescharacteristic
331C2×#103C22×C2911yescharacteristic
332C2×#103C22×C2911yescharacteristic
333C2×#103C22×C2911yescharacteristic
334C2×#103C22×C2911yescharacteristic
335C2×#103C22×C2911yescharacteristic
336C2×#103C22×C2911yescharacteristic
337C2×C22⋊C8C22×C2911yescharacteristic
338C2×#97C22×C2911yescharacteristic
339C2×C4×C8C22×C2911yescharacteristic
340#400—21no—
341#398—21no—
342#396—21no—
343#396—21no—
344#391C22×C2911yescharacteristic
345#389—21no—
346#389C22×C2911yescharacteristic
347#389C22×C2911yescharacteristic
348#389C22×C2911yescharacteristic
349#388—21no—
350#388—21no—
351#387—21no—
352#384C22×C2911yescharacteristic
353#380C22×C2911yescharacteristic
354#380C22×C2911yescharacteristic
355C4×C4⋊C4C22×C2911yescharacteristic
356C4×C22⋊C4C22×C2911yescharacteristic
357#340C22×C2911yescharacteristic
358#340C22×C2911yescharacteristic
359#340C22×C2911yescharacteristic
360#340C22×C2911yescharacteristic
361#340C22×C2911yescharacteristic
362#340C22×C2911yescharacteristic
363#336C22×C2911yescharacteristic
364#336C22×C2911yescharacteristic
365C2×C29—81no—
366C2×C29#255911yescharacteristic
367C2×C29#317411yescharacteristic
368C2×C29#318511yescharacteristic
369C2×C29#331611yescharacteristic
370C2×C29#332011yescharacteristic
371C2×C29#332911yescharacteristic
372C2×C29#333111yescharacteristic
373C22×Q8C23×C2911yescharacteristic
374C22×Q8C23×C2911yescharacteristic
375C23×C4C23×C2911yescharacteristic
376C2×M16—22no—
377C2×M16—41no—
378C2×M16—41no—
379C22×C8C23×C2911yescharacteristic
380C22×C8C23×C2911yescharacteristic
381C22×C8C23×C2911yescharacteristic
382C22×C8C23×C2911yescharacteristic
383C4⋊Q8—22no—
384C4⋊Q8—41no—
385C22⋊Q8—22no—
386C22⋊Q8—22no—
387C22⋊Q8—41no—
388C22⋊Q8—41no—
389C4×Q8—22no—
390C4×Q8—41no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4C23×C2911yescharacteristic
402C2×C4⋊C4C23×C2911yescharacteristic
403C2×C4⋊C4C23×C2911yescharacteristic
404C2×C4⋊C4C23×C2911yescharacteristic
405C2×C4⋊C4C23×C2911yescharacteristic
406C2×C4⋊C4C23×C2911yescharacteristic
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4D4×C2911yescharacteristic
412C2×C22⋊C4D4×C2911yescharacteristic
413C2×C42—21no—
414C2×C42—21no—
415C2×C42C23×C2911yescharacteristic
416C2×C42C23×C2911yescharacteristic
417#106—22no—
418#106—41no—
419#103—22no—
420#103—22no—
421#103—22no—
422#103—22no—
423#103—22no—
424#103—41no—
425#103—41no—
426#103—41no—
427C22⋊C8—22no—
428#97—41no—
429C4×C8—41no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95D4×C2911yescharacteristic
439#95D4×C2911yescharacteristic
440C29#2907011yescharacteristic, direct product factor, Sylow
441C24C2×D4×C2911yescharacteristic
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8#41×C2912yes—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4C2×D4×C2911yescharacteristic
469C22×C4C2×D4×C2911yescharacteristic
470C22×C4C2×D4×C2911yescharacteristic
471C22×C4C2×D4×C2911yescharacteristic
472C22×C4C2×D4×C2911yescharacteristic
473C22×C4C24×C2911yescharacteristic
474M16—44no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8#41×C2912yes—
486C2×C8#41×C2912yes—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—42no—
499C4⋊C4—42no—
500C4⋊C4—42no—
501C4⋊C4—42no—
502C4⋊C4—42no—
503C4⋊C4—42no—
504C4⋊C4—42no—
505C4⋊C4—81no—
506C4⋊C4—81no—
507C4⋊C4—81no—
508C4⋊C4#41×C2912yes—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—42no—
512C22⋊C4—42no—
513C22⋊C4—81no—
514C22⋊C4—81no—
515C42—21no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42—42no—
520C42—81no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23C22×D4×C2911yescharacteristic
529Q8—22no—
530Q8—22no—
531Q8—41no—
532Q8—41no—
533Q8—41no—
534Q8—41no—
535Q8—41no—
536Q8—41no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4C29×#13712yes—
579C2×C4C29×#13712yes—
580C2×C4C2×#41×C2911yescharacteristic
581C2×C4C2×#41×C2911yescharacteristic
582C2×C4C2×#41×C2911yescharacteristic
583C2×C4C2×#41×C2911yescharacteristic
584C2×C4C29×H(5,𝔽2)11yescharacteristic
585C2×C4C29×H(5,𝔽2)11yescharacteristic
586C8—22no—
587C8—22no—
588C8—41no—
589C8—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22C29×#53211yescharacteristic
598C22C29×#54611yescharacteristic
599C22C29×#54611yescharacteristic
600C22C2×C29×#13711yescharacteristic
601C22C2×C29×#13711yescharacteristic
602C22C29×#57711yescharacteristic
603C22C29×#57711yescharacteristic
604C4—22no—
605C4—22no—
606C4—41no—
607C4—42no—
608C4—41no—
609C4—41no—
610C4—42no—
611C4—81no—
612C4—81no—
613C4—81no—
614C4—81no—
615C4—81no—
616C4—81no—
617C4C29×#52911yescharacteristic
618C4C29×#53811yescharacteristic
619C4C29×#55311yescharacteristic
620C4C29×#55311yescharacteristic
621C2—81no—
622C2C29×#255911yescharacteristic
623C2C29×#317411yescharacteristic
624C2C29×#318511yescharacteristic
625C2C29×#331611yescharacteristic
626C2C29×#332011yescharacteristic
627C2C29×#332911yescharacteristic
628C2C29×#333111yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC24×C29C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C4×C22⋊C4×C29 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C29×#2100C2semidirect
4. C29×#2043C2semidirect
7. C29×#1956C2semidirect
8. C29×#1941C2semidirect
9. C29×#1935C2semidirect
10. C29×#1927C2semidirect
13. C29×#1865C2semidirect
14. C29×#1763C2semidirect
206. #29070C29direct (N × H)
278. #2100C2×C29semidirect
279. #2043C2×C29semidirect
282. #1956C2×C29semidirect
283. #1941C2×C29semidirect
284. #1935C2×C29semidirect
285. #1927C2×C29semidirect
288. #1865C2×C29semidirect
289. #1763C2×C29semidirect
440. C29#29070direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C29×#24972
C29×#24292
C29×#21002
C29×#20432
C29×#20352
C29×#19562
C29×#19412
C29×#19352
C29×#19272
C29×#18942
C29×#18652
C29×#17632
C29×#17532
#2907029